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This paper introduces a new formulation for stochastic optimal control andstochastic dynamic optimization that ensures safety with respect to state andcontrol constraints. The proposed methodology brings together concepts such asForward-Backward Stochastic Differential Equations, Stochastic BarrierFunctions, Differentiable Convex Optimization and Deep Learning. Using theaforementioned concepts, a Neural Network architecture is designed for safetrajectory optimization in which learning can be performed in an end-to-endfashion. Simulations are performed on three systems to show the efficacy of theproposed methodology.

Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs